Cremona's table of elliptic curves

2040 = 2³ · 3 · 5 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 17+	Signs for the Atkin-Lehner involutions
Class	2040m	Isogeny class
Conductor	2040	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-510000 = -1 · 24 · 3 · 54 · 17	Discriminant
Eigenvalues	2- 3- 5+  0 -4 -2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,9,-30]	[a1,a2,a3,a4,a6]
Generators	[11:39:1]	Generators of the group modulo torsion
j	4499456/31875	j-invariant
L	3.298735483821	L(r)(E,1)/r!
Ω	1.4626180856031	Real period
R	2.255363526741	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4080a1 16320l1 6120l1 10200e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2040m1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	-	+	0	-4	-2	+	4	0	-6	-4	2	-2	-4	-12	-6	4	-10	-4	8	6	4	-16	-6	14

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Quadratic twists for elliptic curve 2040m1

-4	8	-3	5	-7	17
4080a1	16320l1	6120l1	10200e1	99960cu1	34680bi1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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